| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.63 |
| Score | 0% | 53% |
If a rectangle is twice as long as it is wide and has a perimeter of 30 meters, what is the area of the rectangle?
| 50 m2 | |
| 162 m2 | |
| 32 m2 | |
| 2 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 30 meters so the equation becomes: 2w + 2h = 30.
Putting these two equations together and solving for width (w):
2w + 2h = 30
w + h = \( \frac{30}{2} \)
w + h = 15
w = 15 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 15 - 2w
3w = 15
w = \( \frac{15}{3} \)
w = 5
Since h = 2w that makes h = (2 x 5) = 10 and the area = h x w = 5 x 10 = 50 m2
In a class of 33 students, 12 are taking German and 14 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 19 | |
| 10 | |
| 25 | |
| 22 |
The number of students taking German or Spanish is 12 + 14 = 26. Of that group of 26, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 26 - 3 = 23 who are taking at least one language. 33 - 23 = 10 students who are not taking either language.
A machine in a factory has an error rate of 8 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 211.2 | |
| 81.6 | |
| 99.4 | |
| 111.7 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{8}{100} \) x 6 = \( \frac{8 \times 6}{100} \) = \( \frac{48}{100} \) = 0.48 errors per hour
So, in an average hour, the machine will produce 6 - 0.48 = 5.52 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 5.52 = 99.4 error free parts were produced yesterday.
If all of a roofing company's 6 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 4 complete crews out on jobs?
| 6 | |
| 16 | |
| 1 | |
| 13 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 6 workers at the company now and that's enough to staff 2 crews so there are \( \frac{6}{2} \) = 3 workers on a crew. 4 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 4 x 3 = 12 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 12 - 6 = 6 new staff for the busy season.
If a mayor is elected with 72% of the votes cast and 32% of a town's 25,000 voters cast a vote, how many votes did the mayor receive?
| 5,680 | |
| 6,800 | |
| 5,360 | |
| 5,760 |
If 32% of the town's 25,000 voters cast ballots the number of votes cast is:
(\( \frac{32}{100} \)) x 25,000 = \( \frac{800,000}{100} \) = 8,000
The mayor got 72% of the votes cast which is:
(\( \frac{72}{100} \)) x 8,000 = \( \frac{576,000}{100} \) = 5,760 votes.